A recent study (data extracted from E. J. Boyland et al., "Food Choice and Overconsumption: Effect of a Premium Sports Celebrity Endorser," Journal of Pediatrics, March 13, 2013, bit.ly/16NR4Bi) found that 51 children who watched a commercial for Walker Crisps (potato chips) featuring a long-standing sports celebrity endorser ate a mean of 36 grams of Walker Crisps as compared to a mean of 25 grams of Walker Crisps for 41 children who watched a commercial for an alternative food snack. Suppose that the sample standard deviation for the children who watched the sports celebrity-endorsed Walker Crisps commercial was 21.4 grams and the sample standard deviation for the children who watched the alternative food snack commercial was 12.8 grams.

a. Assuming that the population variances are equal and a = 0.05, is there evidence that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity-endorsed Walker Crisps commercial?

b. Assuming that the population variances are equal, construct a 95% confidence interval estimate of the difference between the mean amount of Walker Crisps eaten by children who watched the sports celebrity-endorsed Walker Crisps commercial and children who watched the alternative food snack commercial. .